Introduction to Options





Kerry Back

Options and Open Interest

  • A financial option is a right to buy or sell a financial security.

  • The right trades separately from the (underlying) security and usually even on a different exchange.

  • The rights are not (usually) issued by the companies who issue the underlying securities.

    • Instead, the rights are created when someone buys one from someone else.
    • Open interest is the number that exist at any time.

Example

  • When a contract is first opened for trading, open interest is zero.
  • Suppose Andy buys a contract from Chloe, and Brooke buys a contract from David.
    • Longs = Andy and Brooke
    • Shorts = Chloe and David
    • Open interest = 2

  • Suppose Andy then sells a contract to David.
    • Andy: long + short = no position
    • David: short + long = no position
    • Longs = Brooke
    • Shorts = Chloe
    • Open interest = 1

Clearinghouse

  • The long party has an option. The short party has an obligation.
  • After a trade is made, the option clearinghouse steps in the middle and becomes the counterparty to both sides.

Hedging, speculation, and income

  • You pay upfront to acquire an option.
    • The amount you pay is called the option premium.
    • It is not part of the contract but instead is determined in the market (like a stock price).
  • You buy options to hedge or to speculate. You sell options for income.
  • Sellers of options need to have sufficient equity in their accounts (margin). A buyer needs enough cash to pay the premium but no more (like buying a stock).

Calls, puts, and strikes

  • A call option gives the holder the right to buy an asset at a pre-specified price.

  • A put option gives the holder the right to sell an asset at a pre-specified price.

  • The pre-specified price is called the exercise price or strike price.

American and European

  • An option is valid for a specified period of time, the end of which is called its expiration date or maturity date.

  • Most financial options can be exercised at any time the owner wishes, prior to maturity. Such options are called American.

  • There are some options that can only be exercised on the maturity date. They are called European. Both types are traded on both continents.

Moneyness

  • Borrowing language from horse racing, we say a call is

    • in the money if the underlying price is above the strike,
    • at the money if the underlying price equals the strike
    • out of the money if the underlying price is below the strike
  • The reverse for puts

  • Also, “deep in the money” and “deep out of the money”

Value of a call at maturity

  • At maturity, the value of a call is

\[\begin{cases} 0 & \text{if underlying < strike}\\ \text{underlying} - \text{strike} & \text{if underlying > strike} \end{cases} \]

  • Equivalently, the value of a call is

\[\max(\text{underlying price}-\text{strike}, 0)\]

Value of a call at maturity

With strike = 50,

Value of a put at maturity

  • At maturity, the value of a put is

\[\begin{cases} \text{strike} - \text{underlying} & \text{if underlying < strike}\\ 0 & \text{if underlying > strike} \end{cases} \]

  • Equivalently, the value of a put is

\[\max(\text{strike}-\text{underlying price}, 0)\]

Value of a put at maturity

With strike = 50,